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Some Laws of Urban Traffic Dynamics: Analysis, Physical Evidence and Control Applications

Some Laws of Urban Traffic Dynamics: Analysis, Physical Evidence and Control Applications. Carlos F. Daganzo U.C. Berkeley Center for Future Urban Transport www.its.berkeley.edu/volvocenter/. References.

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Some Laws of Urban Traffic Dynamics: Analysis, Physical Evidence and Control Applications

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  1. Some Laws of Urban Traffic Dynamics: Analysis, Physical Evidence and Control Applications Carlos F. Daganzo U.C. Berkeley Center for Future Urban Transport www.its.berkeley.edu/volvocenter/

  2. References Daganzo, C.F. (1996) “The nature of freeway gridlock and how to prevent it" in Transportation and Traffic Theory, Proc. 13th Int. Symp. Trans. Traffic Theory (J.B. Lesort, ed) pp. 629 646, Pergamon Elsevier, Tarrytown, N.Y. Daganzo, C.F. (2006) “On the variational theory of traffic flow: well-posedness, duality and applications” Networks and Heterogeneous Media 1(4) 601-619. Daganzo, C.F. (2007) “Urban gridlock: macroscopic modeling and mitigation approaches” Transportation Research B 41, 49-62; with “corrigendum” Transportation Research Part B 41, 379. Daganzo, C.F. and Geroliminis, N. (2008) “An analytical approximation for the macroscopic fundamental diagram of urban traffic” Transportation Research Part B, available on line. Geroliminis N., Daganzo C.F. (2007a) “Macroscopic modeling of traffic in cities” 86th Annual Meeting Transportation Research Board, Washington D.C. Geroliminis, N. and Daganzo, C.F. (2007b) “Existence of urban-scale macroscopic fundamental diagrams: some experimental findings” Working paper, Volvo Center of Excellence on Future Urban Transport, Univ. of California, Berkeley, CA (Transportation Research Part B available on line). 2

  3. L x T Definitions Flow, q = VKT / TL (veh/hr) Density, k = VHT / TL (veh/km) Speed, v = VKT / VHT (km/hr) C-rate, f = Completions / TL (veh/km-hr) (Daganzo, 1996)

  4. Flow, q qmax, Capacity d, kms per completion C-rate, f fmax k0 Density,k Max completion rate Optimum Density Link Laws • (q, k, v) related by FD • q / f = d • Optimal density (Capacity; Max C-rate) (Daganzo, 2007)

  5. Lj Lj = L dj = d kj, qj, vj, fj Composition: J Identical Links (Daganzo, 2007)

  6. Known Result for Ring Roads • Assume: multiple blocks; arbitrary block lengths and widths; arbitrary signal settings; conserved vehicles. • Theorem: If traffic behaves according to variational theory, the ring road exhibits a concave MFD.

  7. Flow Jensen’s inequality: q≤ Q(k) ( ki , qi ) q If vi~ constant: q~Q(k) f~Q(k) / d ( ki, qi) d f C-rate Density Conjectures Network of identical links: • Real Networks: • An MFD exists • Trip completions / Network flow ~ Constant (Daganzo, 2007)

  8. San Francisco Simulation: No Control Outflow Vehicle Accumulation (Geroliminis & Daganzo, 2007a)

  9. Real World Experiment: Site Description • Fixed sensors 500 ultrasonic detectors • Occupancy and Counts per 5min • Mobile sensors 140 taxis with GPS • Time and position • Other relevant data (stops, hazard lights, blinkers etc) • Geometric data Road maps (detector locations, link lengths, intersection control, etc.) 10 km2 (Dec. 2001 data) (Geroliminis & Daganzo, 2007b)

  10. Real World Experiment: The Demand Occupancy by time-of-day Flow by time-of-day (Geroliminis & Daganzo, 2007b)

  11. Real World Experiment: The Detectors qi (dimensionless) oi (%)

  12. Real World Experiment: The Detectors (Geroliminis & Daganzo, 2007b)

  13. Real World Experiment:Taxis Conjecture: Passenger carrying taxis use the same parts of the network as cars Then: (Geroliminis & Daganzo, 2007b)

  14. Filters to determine full vs. empty taxis • A stop is a passenger move, if: • hazard lights are ON or • parking brake is used or • left blinker is ON and taxi stops > 45 sec or • speed < 3 km/hr for >60sec • A trip is valid if: • trip duration > 5 min and length > 1.5 km and • trip distance < 2 × “Euclidean distance” (Geroliminis & Daganzo, 2007b)

  15. Illustration of Filter Results (Geroliminis & Daganzo, 2007b)

  16. Illustration of Filter Results (Cont.) (Geroliminis & Daganzo, 2007b)

  17. Real World Experiment:Taxis Conjecture: Passenger carrying taxis use the same parts of the network as cars Then: (Geroliminis & Daganzo, 2007b)

  18. Real World Experiment: Results (Geroliminis & Daganzo, 2007b)

  19. n Aggregate Dynamics Given : inflow qin Output: e = G(n) qin e = G(n) n (Daganzo, 2007)

  20. Finding:Effect of Control No Control With Control Trips Ended Time Trips Ended Time Restrict vehicles from entering (Geroliminis & Daganzo, 2007a)

  21. Ongoing Work: San Francisco (Daganzo & Geroliminis, 2007)

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